This invention relates to the use of a Discrete Fourier Transform (DFT) to provide multi-dimensional analysis of molecular specimens.
Working with multi-dimensional data such as the processing of Nuclear Magnetic Resonance (NMR) or Ion Cyclotron Resonance (ICR) data requires the manipulation of data sets in the gigabyte range. Heretofore, this type of data was generally processed using Fast Fourier Transform (FFT) techniques. In a two-dimensional application such as NMR or ICR, a set of time domain waveforms are generated and these waveforms are then represented in terms of frequency content by computing the correlation between a specific group of reference frequencies and each time domain waveform in the set. The degree of correlation between a specific reference frequency and a time domain waveform is known as the spectral content of the waveform at that specific frequency. The spectral content of a waveform for a group of reference frequencies is called the frequency spectrum or simply the spectrum of the time domain waveform.
In a two dimensional FFT analysis, a set of time domain waveforms are generated and the waveform is then frequency transformed using specific reference frequencies. The spectral amplitude at a particular reference frequency of each waveform in the set forms a group of values or data points which can be treated as a frequency domain waveform. A spectral analysis of these primary groups of frequency domain waveforms is performed to produce a second frequency transformation. In the FFT analysis the combined process of a primary transform on the time domain waveforms in the set and a secondary transform on the resultant frequency domain waveforms is called a two-dimensional frequency transformation. It is also possible to continue this process to higher dimensions by further transforming the secondary group of frequency waveforms.
In performing a two-dimensional FFT process, a frequency interval, the number of primary reference frequencies and the desired resolution is first decided upon. The spectrum of a single time domain waveform in the set is then computed with the restriction that all spectral amplitudes are calculated simultaneously. The advantage of the FFT procedure as the name implies is the speed by which each individual waveform can be transformed. There are, however, other disadvantages associated with the FFT procedure. It is necessary to determine the spectral content of each waveform in the set at all frequencies within the selected band of frequencies, even though some of the frequencies are of no interest. A further disadvantage associated with the FFT process is that all primary transforms must be completed before the secondary transforms can be started. This requires a relatively large amount of memory to store the primary transform data. Additionally, the primary transform data, if stored on disk, is not entered in the proper order needed to perform the transforms in the second dimension. Accordingly, a time consuming data moving operation known as corner turning or transposing must be carried out prior to executing the transforms in the second dimension. Where NMR is used to examine patients, a lengthy examination period can be both tiring and trying on the patient.